Tsunami occurrence and invasive tsunami at a local area in the circum‐Pacific seismic zone were studied as a Poisson process. The tsunami height at Osaka, Japan, was related to tsunami magnitude. The exceedence frequency of invaded tsunami at Osaka showed a good fitness to the Poisson process. However, an adapted process should be introduced for exceedence frequency of tsunami occurrence in the western Pacific. The exceedence probability of invasive tsunami at Osaka was shown as a function of tsunami magnitude on a diagram with a parameter of the time period. The obtained result might be useful for the planning of coastal area, warning of invasive tsunami, and designing coastal structures as protection within the scope of tsunami economics.